Ultrasound in Med. & Biol., Vol. 40, No. 4, pp. 828–836, 2014 Copyright Ó 2014 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/$ - see front matter
http://dx.doi.org/10.1016/j.ultrasmedbio.2013.04.016
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Original Contribution RELATIVE BLOOD FLOW CHANGES MEASURED USING CALIBRATED FREQUENCY-WEIGHTED DOPPLER POWER AT DIFFERENT HEMATOCRIT LEVELS SEAN WALLACE,* NICOLA LOGALLO,y KASHIF W. FAIZ,z CHRISTIAN LUND,* RAINER BRUCHER,x and DAVID RUSSELL* * Department of Neurology, Oslo University Hospital, Rikshospitalet, Oslo, Norway; y Department of Neurology, Haukeland University Hospital, Bergen, Norway; z Department of Neurology, Akershus University Hospital, Oslo, Norway; and x Department of Medical Engineering, University of Applied Sciences, Ulm, Germany (Received 10 October 2012; revised 14 April 2013; in final form 21 April 2013)
Abstract—In theory, the power of a trans-cranial Doppler signal may be used to measure changes in blood flow and vessel diameter in addition to velocity. In this study, a flow index (FI) of relative changes in blood flow was derived from frequency-weighted Doppler power signals. The FI, plotted against velocity, was calibrated to the zero intercept with absent flow to reduce the effects of non-uniform vessel insonation. An area index was also calculated. FIs were compared with actual flow in four silicone tubes of different diameter at increasing flow rates and increasing hematocrit (Hct) in a closed-loop phantom model. FI values were strongly correlated with actual flow, at constant Hct, but varied substantially with changes in Hct. Percentage changes in area indexes, relative to the 4-mm tube, were strongly correlated with tube cross-sectional area. The implications of these results for in vivo use are discussed. (E-mail: [email protected]) Ó 2014 World Federation for Ultrasound in Medicine & Biology. Key Words: Trans-cranial Doppler, Flow index, Area index, Doppler power, Hematocrit.
INTRODUCTION
some form of vessel diameter measurement is made together with velocity recordings. Such measurements are, however, difficult in cerebral vessels, as the accuracy of imaging techniques is restricted by the small dimensions of the vessels and any diameter changes that occur. A method that potentially avoids the need for direct measurement of CSA uses changes in the power of the Doppler signal. It has been postulated that each red blood cell (RBC) contributes equally to the power of the reflected Doppler signal, provided the vessel is insonated with uniform intensity. The power of the received signal should therefore be related to the number of RBCs and, hence, the volume of blood within the sample volume (Arts and Roevros 1972). The reflected signal power is, however, also affected by variations in the spatial positioning of RBCs relative to each other. The random positions of RBCs, or aggregates of RBCs, in the Doppler sample volume produces speckling in the received Doppler power. With non-turbulent flow, because of the large number of RBCs, there is an average distance between the randomly positioned cells at each hematocrit (Hct). The received Doppler power should depend on the Hct, as well as flow velocity and vessel lumen size.
Trans-cranial Doppler (TCD) is a well-established, noninvasive method commonly used to measure blood flow velocity (BFV) in the major intracranial vessels. However, a major limitation of this method is its inability to measure blood flow directly, because blood flow in a vessel is determined by both BFV and vessel cross-sectional area (CSA). In the clinical setting, information regarding changes in blood flow is inferred from changes in BFVon the assumption that vessel CSA remains constant. Several studies have validated a relationship between BFV and blood flow in specific clinical situations (Batton et al. 1983; Bishop et al. 1986; Greisen et al. 1984; Haaland et al. 1994; Hansen et al. 1983; Larsen et al. 1994; Lindegaard et al. 1987; Trivedi et al. 1997). In most clinical settings, however, this assumption is either incorrect or unproven (Kontos 1989; Sonesson and Herin 1988; Weyland et al. 1994). This potential source of error may be eliminated if Address correspondence to: Sean Wallace, Department of Neurology, Oslo University Hospital, Rikshospitalet, 0424 Oslo, Norway. E-mail: [email protected] Conflicts of Interest: The authors have indicated that they have no conflicts of interest regarding the content of this article. 828
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Because of the specific velocity patterns of blood flow within a vessel, the Doppler signal comprises a spectrum of frequencies, each relating to a specific velocity of red blood cells and their aggregates within the blood flow profile. If the axial length of the sample volume does not change, then the sum of the power levels of these frequencies should be proportional to the volume of blood within the sample volume (Hatab et al. 1997). Given that volume flow (mL/min) 5 mean velocity 3 cross-sectional area F 5 Vmean 3A
X
Pi 3fi
(2)
An area index (AI), which can be used to determine relative changes in CSA, may then be calculated by dividing the FI by the mean or maximum velocity of the Doppler spectrum: AI 5 FI=Vmax :
Hct values greater than 28% should also be associated with speckle, and are associated with a decrease in the Doppler signal power caused by clumping of RBCs and multi-reflections of the Doppler signal (Oates 2001; Atkinson and Woodcock 1982). The aims of this in vitro study were, first, to determine the accuracy of flow index and area index measurements with off-set calibration when used to assess relative changes in blood flow and cross-sectional area and, second, to study the effects of hematocrit changes on these measurements.
(1)
a flow index (FI) can be calculated from the sum of the products of Doppler frequency (f i) and corresponding power signal (Pi): FI 5
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(3)
The correlation between the frequency-weighted power (FWP) and blood flow is based on the power of the insonating beam reflected from within the vessel. FIs are therefore affected by a number of factors, besides speckle, that cause a non-uniform intensity distribution of the ultrasound beam within the vessel (Deverson and Evans 2000a, 2000b; Fry and Barger 1978; Hatab et al. 1997). This, in turn, influences the correlation between FI and Vmax. The resulting FI/Vmax correlation line will have a slope that is off-set, so that it does not pass through the zero axis intercept. This line should pass through the zero intercept, as there is no flow when velocity in the vessel is zero. This off-set may, in theory, be corrected by calibration of the FI/V correlation line to the zero intercept, thereby reducing the effects of the aforementioned confounding factors. The use of FWP to assess relative blood flow changes assumes not only that on average each RBC contributes to the reflected Doppler power, but also that the concentration of RBCs remains constant. The number of RBCs contributing to the reflected signal is dependent on both the volume of blood within the sample volume and the Hct, where Hct is defined as the percentage volume of blood occupied by RBCs. There is a linear relationship between the reflected Doppler signal power and RBC concentration at low Hct values, with maximal power at a Hct of approximately 28% (Mo et al. 1994; Oates 2001; Yuan and Shung 1988). This is lower than physiologic levels, which are normally around 40%.
METHODS Closed-loop phantom Studies were performed using a closed-loop system of silicon tubes (RCT High-Flexible, Reichelt, Heidelberg, Germany) containing saline and human whole blood. The blood, which had exceeded its clinical usage date the previous day, was obtained from the local blood transfusion bank. Non-pulsatile, forward flow was generated using a digital roller pump (Ismatec, MCP Process Pump, Glattburg, Switzerland). The blood was heparinized, kept at constant flow and continuously filtered using a 40-mmol micro-filter (BMAF-A arterial filter 40 mm, Medos Medizintechnik, Stolberg, Germany), to prevent contamination by either gas bubbles or solid microparticles. A Windkessel function was incorporated into the system. A constant temperature of 32 C was maintained within the closed-loop system by passing the tubing through a heated water bath. Although lower than normal, this temperature approximates physiologic conditions while providing some protection to the red blood cells during the studies. It has clinical significance, as it is used during cardiac surgery and hypothermic treatment of hypoxic brain injuries. The temperature was continuously monitored using a digital thermometer (Metrawatt M4051, BBC Goerz, Vienna, Austria). Recordings Flow index measurements were made at flow rates of 150, 240 and 320 mL/min by insonating silicone tubes with inner diameters similar to those of the middle cerebral artery of children and adults: 1.5, 2, 3 and 4 mm with a wall thickness of 0.5 mm. The tubes were insonated at an angle of 45 , with two-channel TCD instrumentation, 2-MHz insonation frequency, and a peak repetition frequency of 8 kHz (DWL Compumedics, Singen, Germany). The tubes were insonated through a 0.5-cm Plexiglas wall to mimic the effects of the human skull acoustic impedance Plexiglas 5 3.2 kg/m2 s; cortical bone 5 3.38 kg/m2 s (Bloomfield et al. 2000; Smitmans 2002). The transducer was secured with a specially designed Plexiglas holder. Each of the four tubes was
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insonated within a water bath with constant power and gain settings. To maximize the received Doppler power signals, for all recordings, the axial length of the sample volume was initially set to 4 mm when each of the respective tubes was placed under the transducer. It was then positioned until the maximum Doppler power signal was obtained using range gating. For Doppler power measurements, the axial length of the sample volume was extended to 10 mm for the 2-, 3- and 4-mm tubes and to 8 mm for the 1.5-mm tube. Optimizing the position of the sample volume enabled us to assume that the maximum beam intensity lay within the central region of the parabolic flow in the tube being studied, that is, the area of highest BFVs. Maximization of signal power was also necessary to ensure that the insonating beam intensity distribution was approximately equal for all tubes studied (Deverson and Evans 2000a). The high-pass frequency filter was set to a standard setting of 100 Hz. The measurements were recorded and averaged over a period of 10 s. Frequency-weighted firstmoment calculations of Doppler power were made using specially designed software (spectral power estimation within a spectrogram based on a 256-point fast Fourier transform with Blackman windowing and 50% spectral overlap). Velocity was measured and FI values were calculated automatically. Any offset in the FI/Vmax correlation slope was corrected by a calibration that vertically adjusted the line so that the slope passed through the zero intercept for velocity and FI (off-set calibration). Although both Vmax and Vmean provide information on blood flow values, when cross-sectional area is constant, Vmax is less sensitive to high-intensity artifacts in the spectrogram. Vmax values were therefore used to calculate flow and cross-sectional indexes. Relative measurements of change To enable the calculation of relative changes (percentage) in flow and area indexes, the FI value in the largest tube (4-mm diameter) was designated as 100% for each flow rate and Hct. Similarly, the AI values for the 4-mm-diameter tube, at the three flow rates and at each Hct, were designated as 100%. The FIs and AIs calculated for the other tubes were compared with these to determine the relative percentage changes as flow volume increased. Hematocrit values Heparinized whole blood with an initial Hct of approximately 60% from the same batch of AB Rhpositive blood was used for all recordings. The closedloop system was initially filled with 0.9% saline, and all gas bubbles were removed. Heparinized whole blood was added gradually to the system, and an equivalent volume of the blood-saline mixture was removed to
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obtain blood with different Hct values. Extreme care was taken not to introduce gas bubbles as blood was injected. Blood was allowed to flow through the system for at least 3 min before the recordings. Increasing Hct values were measured directly using a centrifuge (Hemokrit 4, Lic Instruments, Stockholm, Sweden) and Hct graph (Heræus Sepatech, Osterode/Harz, Germany). Doppler measurements were then carried out at the three different flow rates (150, 240 and 320 mL/min) and four different hematocrits (10, 20, 29 and 42%). Hematocrit was re-measured at the end of each set of recordings to ensure that it had not changed. RESULTS A strong linear correlation between calculated FI values and actual flow was found for each of the four insonated tube sizes at flow values of 150, 240 and 320 mL/ min (Fig. 1a–d). Each of the four graphs represents one of the defined Hct values (10%, 20%, 29% and 42%). Linear dependence was strong for all recordings, with a Pearson correlation coefficient greater than 0.95 for each tube (Table 1). The FI values obtained from the recordings were arbitrary, relative values and, as such, are not units are not given. The percentage change in FI values also correlated strongly and linearly with the actual flow measurements in all four tubes, at all flow rates and Hct values (all Pearson correlation coefficients .0.99). The correlation lines plotted for FI values and actual flow did not maintain a consistent position relevant to each other in the four graphs in Figure 1. For each new set of measurements, the relevant tube had to be placed below the fixed transducer. Despite the efforts described above, it was impossible to ensure that each of the tubes was in exactly the same position. Some small variation in tube position was inevitable, and this may have affected the power of the reflected Doppler signal. The speckling effect of RBCs on the backscattered Doppler echoes may also influence the Doppler power levels reflected at each Hct value, which may explain the random ordering of the plots of correlation between flow index and flow (Fig. 1). The calculated AI values varied by up to 8% as flow volume increased from 150 to 320 mL/min, even though both Hct and tube CSA remained constant. The calculated percentage changes in AI, normalized to the 4-mm tube values, exhibited a much smaller degree of deviation from actual CSA values (range: 0–2%, mean level of variation: 0.4%) (Table 2) when Hct was constant. A strong linear correlation between these relative changes in AI and the corresponding CSA values for all tubes was also observed (all Pearson correlation coefficients .0.99, all associated significance measures ,0.01). Figure 2(e–h) illustrates this linear dependence.
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Fig. 1. Correlation between flow index and flow (mL/min). The graphs indicate a strong correlation between calculated flow index (FI) values and actual flow (150, 240 and 320 mL/min) in the four tubes of different size. Each graph represents one of the defined hematocrit values: (a) 10%, (b) 20%, (c) 29%, (d) 42%. Hematocrits and tube diameters were constant for each set of recordings. Pearson correlation values are .0.99 for all plots. C 5 1.5-mm tube, : 5 2-mm tube, - 5 3-mm tube, A 5 4-mm tube.
The variation in FI values when Hct was increased from 10% to 42% was substantial; ranging from 25% in the 3- and 4-mm tubes to 76% in the 1.5-mm tube, even though both flow and tube CSA remained constant (Fig. 3i–l). Plots of either FI or AI versus Hct revealed an initial increase in the respective indices as Hct increased from 10% to 20%. A rise in Hct from 20% to 29% was associated with a reversal of this trend, and all FI values calculated at a Hct of 29% were lower than those calculated at a 20% Hct. A further increase in Hct, from 29% to 42%, was associated, in most of the studies, with a greater decrease in FI values. As Hct rose from 20% to 29%, the average decreases in FI values in the 4-, 3-, 2- and 1.5-mm tubes were 20%,
30%, 26% and 18%, respectively. With a further increase in Hct from 29% to 42%, the FI decreased by an average of 7%, 7.5% and 12% in the 4-, 3- and 2-mm tubes, respectively. For the 1.5-mm tube, there was a comparatively larger decrease in the FI of 28% as Hct rose from 29% to 42%. DISCUSSION This is the first in vitro study to find that calibrated, frequency-weighted TCD signal power measurements may be used to assess relative blood flow and crosssectional area changes. The FI/velocity off-set calibration described in this study minimized the influence of factors that negatively affect how uniformly the vessel is
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Table 1. Pearson linear correlation values (and significance measurements) for FI values versus actual flow for each of the four tube diameters at the four different hematocrit values* Pearson correlation for FI versus flow Diameter (mm) Hematocrit 10 Hematocrit 20 Hematocrit 29 Hematocrit 42 1.5 2 3 4
0.99y 0.98y 1 0.99y
1z 0.99y 1y 1y
1y 1y 0.99 0.99
1z 0.99y 1z 0.99y
* See Figure 1 and main text. y Significant, p $ 0.05. z Significant, p # 0.01.
insonated by the ultrasound beam. We also confirmed that both flow and area indexes are dependent on constant Hct values. The flow index used in this study was derived from an effective average Doppler power at each hematocrit level. Because of the large number of RBCs in the sampling volume there is an average distance between RBCs, and this average distance, varying with hematocrit level, effectively determines Doppler power and the effect of speckle on Doppler power. Plots of flow index versus flow (Fig. 1) revealed a random order of results associated with hematocrit value, which is consistent with the effects of speckle. These results support our definition of a flow index at a constant hematocrit, but also indicate the random results caused by speckle. A number of in vivo studies have used information from the full Doppler power spectrum in an effort to measure flow variation (Aaslid 1987; Aaslid et al. 1989; Poulin and Robbins 1996; Poulin et al. 1996). These studies did not, however, correct for the effects of inhomogeneous vessel insonation on the reflected Doppler power signal and the FI/velocity relationship. The theoretical relationship between Doppler signal power and vessel CSA is, among other things, Table 2. Percentage change in area index versus tube diameter as flow volume increases* Maximal change in area index (%) Diameter (mm) Hematocrit 10 Hematocrit 20 Hematocrit 29 Hematocrit 42 1.5 2 3 4
0 0 0 0
0 1 2 1
0 1 1 1
0 1 1 0
* Each of the 16 values in the table is the maximal percentage change in area index as flow rate increased from 150 to 320 mL/min. For each value, the hematocrit and tube diameter were constant. A relative change in the area index was calculated on the basis of flow index values. The area index values calculated for the 4-mm-diameter tube were designated as the 100% values. The area index values calculated for the other three tubes were normalized to these values.
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dependent on uniform insonation of the vessel. This is necessary to ensure correct weighting of the power signal reflected from RBCs moving at different velocities (Arts and Roevros 1972; Deverson and Evans 2000a; Hatab et al. 1997). In calculation of the FI, the power of the Doppler signals reflected from the various points within the vessel being insonated is weighted according to the Doppler frequency of the beam at each corresponding position. Variations in beam intensity will therefore lead to a variation in the weighting and a distortion of the received Doppler signal. Factors that lead to distortion of the ultrasound beam and, therefore, nonuniform vessel insonation include inhomogeneous tissue layering between the transducer and the vessel and, in particular, the temporal bone, which causes attenuation and refraction of the ultrasound beam and non-uniform insonation of the vessel (Deverson and Evans 2000a; Deverson et al. 2000; Fry and Barger 1978; Hatab et al. 1997). It has been observed that the extent of spectral power distortion is related to the shape of the ultrasound beam across the vessel (Deverson and Evans 2000a, 2000b). A correction factor for non-uniform insonation can be calculated for in vitro measurements when the vessel size is known (Deverson and Evans 2000a, 2000b). This is, however, not possible for in vivo recordings, where the diameter of the vessel is normally not known. We have therefore carried out a calibration of the off-set of the slope describing the correlation between the calculated FI and velocity values. The slope of the curve describing the relationship between these two parameters did not pass through zero with absent flow because of signal damping and the Plexiglas wall, which mimics the effects of the temporal bone on the ultrasound beam. The intercept of the correlation line between FI and maximum velocity V was therefore corrected to zero, with the gradient of the slope remaining unchanged. This is especially important for future clinical studies, as it has been shown that the degree of ultrasound beam distortion varies between patients (Deverson and Evans 2000a, 2000b). An automatic zero-intercept calibration of this correlation is therefore mandatory for each new set of measurements. Flow index and maximum velocity values were used to determine relative changes in cross-sectional area, as F 5 CSA 3 Vmax. We found a strong correlation between relative changes in AI values and corresponding CSAs. This contrasts with the findings of Giller et al. (1998), who found that Doppler spectral power measurements in arbitrary units gave varying AI values. Clinical measurements Potential weaknesses of this method, when applied in the clinical setting, include the effects of high-pass
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Fig. 2. Correlation between percentage change in area index and cross-sectional area (mm2). The graphs reveal that there was a strong correlation between percentage change in area index (AI) and change in cross-sectional area (CSA). Area indexes were calculated for each of the four tubes of different sized. Volume flow and hematocrit remained constant. Percentage changes in area indexes, relative to measurements for the largest (4-mm) tube, were calculated. Pearson linear correlation values are .0.99, with significance at p , 0.01 for all plots. Hematocrit: (e) 10%, (f) 20%, (g) 29%, (h) 42%. , 5 150 mL/min, > 5 240 mL/min, O 5 340 mL/min.
filtering and the need for both a constant Hct value and absolute stability of the transducer position to allow continuous measurement of the maximal Doppler power from the vessel. Movement of the TCD probe will lead to a loss of or decrease in the reflected Doppler power signal. Previous studies have reported that there is one optimal transducer position for the measurement of maximum power values and that the received power falls by more than 25% within 1 mm of this position (Deverson and Evans 2000a). Minimal movements of the transducer during clinical recordings can lead to an incorrect assessment of relative
blood flow changes. It is therefore essential, in the clinical setting, that the probe maintains a position where it measures the maximum reflected Doppler power signal from the vessel. It is hoped that the ongoing development of transducer devices that automatically maintain an optimal Doppler signal will help to resolve this very important problem (von Kruger and Evans 2002), allowing measurements with minimum contributions from voluntary or involuntary patient motion. High-pass filtering is used to attenuate lowfrequency components within the signal, such as those caused by slow vessel wall movement. Filtering will
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Fig. 3. Flow index versus hematocrit. The graphs illustrate the changes in flow indexes with rising hematocrit values, despite constant flow volume and tube diameter. Flow index initially increased and then decreased at hematocrit increased. Tube diameter: (i) 4 mm, (j) 3 mm, (k) 2 mm, (l) 1.5 mm. — 5 320 mL/min, ∙∙∙∙∙ 5 240 mL/min, - - 5 150 mL/min.
therefore have an effect only on the small number of RBCs close to the vessel wall with the lowest velocities. Frequency-weighted Doppler power measurements are focused on the higher velocities in the central part of the vessel lumen, further ensuring that any effect of filtering will be minimal. Indexes of relative blood flow changes based on variations in the ultrasound power reflected from RBCs are also affected by changes in Hct values. The relationship
between Hct and Doppler signal power is complex. At low Hct values, much lower than physiologic values, there is a linear relationship between increasing Hct values and increasing Doppler signal power, as the RBCs individually contribute to the reflected signal power. At higher Hct values, the RBCs begin to aggregate, and the assumption that each RBC is contributing to the reflected ultrasound power is no longer true (Oates 2001). An increase in Hct above 28% leads to a decrease in the received
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Doppler power signal because of a change in the scattering coefficient of the blood. Despite this, it has been postulated that even at higher, physiologic Hct values, the power of the received Doppler power signal can still be used to measure relative changes in blood flow and CSA, provided the Hct remains constant (Deverson and Evans 2000a, 2000b). This hypothesis has, however, not been previously confirmed. Our results clearly indicate that Doppler power is affected by changing Hct values. FI values increased as Hct values rose from 10% to higher values and decreased when Hct increased above 29%. We did, however, find that the calculated FI values were strongly correlated with actual flow within a wide range of constant Hct values, including those in the normal, physiologic range. In most clinical situations, Hct will not change. This may not be the case when TCD is used to monitor intracranial hemodynamics during surgery, where both blood loss and intravenous fluid therapy are common. We have assumed that change in flow values or acceleration of RBCs does not have a significant effect on the reflected Doppler power and its instantaneous spectral distribution. These instantaneous index calculations are based on frequency-weighted power measurements using one fast Fourier transform process within 20 ms. The red blood cell velocities can be assumed to be constant with no significant changes in Doppler frequency. Furthermore, although the echogenicity of blood may vary during pulsatile flow, Doppler power does not vary significantly during pulsatile cycles or changes in flow rates (Paeng et al. 2001). The indexes calculated in this study exhibited a good correlation in a range of different actual flow rates and cross-sectional areas when hematocrit values were constant. Finally, we used the TCD instrumentation to calculate the indexes described because of the specific difficulties involved in measuring changes in blood flow in the relatively small vessels throughout the skull. In this situation the ultrasound transducer can be maintained in an almost constant position at the temporal bone acoustic window. The methods and conclusions can, however, be applied to vascular ultrasound in general, provided the transducer position and, therefore, damping of the ultrasound in the tissue remains constant with respect to the insonated vessel. CONCLUSIONS This is the first in vitro study to find that calibrated, frequency-weighted trans-cranial Doppler signal power measurements may be used to assess relative blood flow and cross-sectional area changes; however, these measurements are dependent on constant hematocrit values.
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Acknowledgments—S. Wallace and N. Logallo each received research grants from the Norwegian Foundation for Health and Rehabilitation.
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Poulin MJ, Liang PJ, Robbins PA. Dynamics of the cerebral blood flow response to step changes in end-tidal PCO2 and PO2 in humans. J Appl Physiol 1996;81:1084–1095. Poulin MJ, Robbins PA. Indexes of flow and cross-sectional area of the middle cerebral artery using Doppler ultrasound during hypoxia and hypercapnia in humans. Stroke 1996;27:2244–2250. Smitmans, Ludger F. Zur Bestimmung akusto-elastischer Eigenschaften von humanem, kortikalem Knochengewebe mit der akustischen Rastermikroskopie. Disertation 2002 Universit€at Martin-Luther Universit€at Halle-Wittenberg, Germany. http://sundoc.bibliothek. uni-halle.de/diss-online/02/03H009/prom.pdf. Sonesson SE, Herin P. Intracranial arterial blood flow velocity and brain blood flow during hypocarbia and hypercarbia in newborn lambs: A validation of range-gated Doppler ultrasound flow velocimetry. Pediatr Res 1988;24:423–426.
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Original Contribution RELATIVE BLOOD FLOW CHANGES MEASURED USING CALIBRATED FREQUENCY-WEIGHTED DOPPLER POWER AT DIFFERENT HEMATOCRIT LEVELS SEAN WALLACE,* NICOLA LOGALLO,y KASHIF W. FAIZ,z CHRISTIAN LUND,* RAINER BRUCHER,x and DAVID RUSSELL* * Department of Neurology, Oslo University Hospital, Rikshospitalet, Oslo, Norway; y Department of Neurology, Haukeland University Hospital, Bergen, Norway; z Department of Neurology, Akershus University Hospital, Oslo, Norway; and x Department of Medical Engineering, University of Applied Sciences, Ulm, Germany (Received 10 October 2012; revised 14 April 2013; in final form 21 April 2013)
Abstract—In theory, the power of a trans-cranial Doppler signal may be used to measure changes in blood flow and vessel diameter in addition to velocity. In this study, a flow index (FI) of relative changes in blood flow was derived from frequency-weighted Doppler power signals. The FI, plotted against velocity, was calibrated to the zero intercept with absent flow to reduce the effects of non-uniform vessel insonation. An area index was also calculated. FIs were compared with actual flow in four silicone tubes of different diameter at increasing flow rates and increasing hematocrit (Hct) in a closed-loop phantom model. FI values were strongly correlated with actual flow, at constant Hct, but varied substantially with changes in Hct. Percentage changes in area indexes, relative to the 4-mm tube, were strongly correlated with tube cross-sectional area. The implications of these results for in vivo use are discussed. (E-mail: [email protected]) Ó 2014 World Federation for Ultrasound in Medicine & Biology. Key Words: Trans-cranial Doppler, Flow index, Area index, Doppler power, Hematocrit.
INTRODUCTION
some form of vessel diameter measurement is made together with velocity recordings. Such measurements are, however, difficult in cerebral vessels, as the accuracy of imaging techniques is restricted by the small dimensions of the vessels and any diameter changes that occur. A method that potentially avoids the need for direct measurement of CSA uses changes in the power of the Doppler signal. It has been postulated that each red blood cell (RBC) contributes equally to the power of the reflected Doppler signal, provided the vessel is insonated with uniform intensity. The power of the received signal should therefore be related to the number of RBCs and, hence, the volume of blood within the sample volume (Arts and Roevros 1972). The reflected signal power is, however, also affected by variations in the spatial positioning of RBCs relative to each other. The random positions of RBCs, or aggregates of RBCs, in the Doppler sample volume produces speckling in the received Doppler power. With non-turbulent flow, because of the large number of RBCs, there is an average distance between the randomly positioned cells at each hematocrit (Hct). The received Doppler power should depend on the Hct, as well as flow velocity and vessel lumen size.
Trans-cranial Doppler (TCD) is a well-established, noninvasive method commonly used to measure blood flow velocity (BFV) in the major intracranial vessels. However, a major limitation of this method is its inability to measure blood flow directly, because blood flow in a vessel is determined by both BFV and vessel cross-sectional area (CSA). In the clinical setting, information regarding changes in blood flow is inferred from changes in BFVon the assumption that vessel CSA remains constant. Several studies have validated a relationship between BFV and blood flow in specific clinical situations (Batton et al. 1983; Bishop et al. 1986; Greisen et al. 1984; Haaland et al. 1994; Hansen et al. 1983; Larsen et al. 1994; Lindegaard et al. 1987; Trivedi et al. 1997). In most clinical settings, however, this assumption is either incorrect or unproven (Kontos 1989; Sonesson and Herin 1988; Weyland et al. 1994). This potential source of error may be eliminated if Address correspondence to: Sean Wallace, Department of Neurology, Oslo University Hospital, Rikshospitalet, 0424 Oslo, Norway. E-mail: [email protected] Conflicts of Interest: The authors have indicated that they have no conflicts of interest regarding the content of this article. 828
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Because of the specific velocity patterns of blood flow within a vessel, the Doppler signal comprises a spectrum of frequencies, each relating to a specific velocity of red blood cells and their aggregates within the blood flow profile. If the axial length of the sample volume does not change, then the sum of the power levels of these frequencies should be proportional to the volume of blood within the sample volume (Hatab et al. 1997). Given that volume flow (mL/min) 5 mean velocity 3 cross-sectional area F 5 Vmean 3A
X
Pi 3fi
(2)
An area index (AI), which can be used to determine relative changes in CSA, may then be calculated by dividing the FI by the mean or maximum velocity of the Doppler spectrum: AI 5 FI=Vmax :
Hct values greater than 28% should also be associated with speckle, and are associated with a decrease in the Doppler signal power caused by clumping of RBCs and multi-reflections of the Doppler signal (Oates 2001; Atkinson and Woodcock 1982). The aims of this in vitro study were, first, to determine the accuracy of flow index and area index measurements with off-set calibration when used to assess relative changes in blood flow and cross-sectional area and, second, to study the effects of hematocrit changes on these measurements.
(1)
a flow index (FI) can be calculated from the sum of the products of Doppler frequency (f i) and corresponding power signal (Pi): FI 5
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The correlation between the frequency-weighted power (FWP) and blood flow is based on the power of the insonating beam reflected from within the vessel. FIs are therefore affected by a number of factors, besides speckle, that cause a non-uniform intensity distribution of the ultrasound beam within the vessel (Deverson and Evans 2000a, 2000b; Fry and Barger 1978; Hatab et al. 1997). This, in turn, influences the correlation between FI and Vmax. The resulting FI/Vmax correlation line will have a slope that is off-set, so that it does not pass through the zero axis intercept. This line should pass through the zero intercept, as there is no flow when velocity in the vessel is zero. This off-set may, in theory, be corrected by calibration of the FI/V correlation line to the zero intercept, thereby reducing the effects of the aforementioned confounding factors. The use of FWP to assess relative blood flow changes assumes not only that on average each RBC contributes to the reflected Doppler power, but also that the concentration of RBCs remains constant. The number of RBCs contributing to the reflected signal is dependent on both the volume of blood within the sample volume and the Hct, where Hct is defined as the percentage volume of blood occupied by RBCs. There is a linear relationship between the reflected Doppler signal power and RBC concentration at low Hct values, with maximal power at a Hct of approximately 28% (Mo et al. 1994; Oates 2001; Yuan and Shung 1988). This is lower than physiologic levels, which are normally around 40%.
METHODS Closed-loop phantom Studies were performed using a closed-loop system of silicon tubes (RCT High-Flexible, Reichelt, Heidelberg, Germany) containing saline and human whole blood. The blood, which had exceeded its clinical usage date the previous day, was obtained from the local blood transfusion bank. Non-pulsatile, forward flow was generated using a digital roller pump (Ismatec, MCP Process Pump, Glattburg, Switzerland). The blood was heparinized, kept at constant flow and continuously filtered using a 40-mmol micro-filter (BMAF-A arterial filter 40 mm, Medos Medizintechnik, Stolberg, Germany), to prevent contamination by either gas bubbles or solid microparticles. A Windkessel function was incorporated into the system. A constant temperature of 32 C was maintained within the closed-loop system by passing the tubing through a heated water bath. Although lower than normal, this temperature approximates physiologic conditions while providing some protection to the red blood cells during the studies. It has clinical significance, as it is used during cardiac surgery and hypothermic treatment of hypoxic brain injuries. The temperature was continuously monitored using a digital thermometer (Metrawatt M4051, BBC Goerz, Vienna, Austria). Recordings Flow index measurements were made at flow rates of 150, 240 and 320 mL/min by insonating silicone tubes with inner diameters similar to those of the middle cerebral artery of children and adults: 1.5, 2, 3 and 4 mm with a wall thickness of 0.5 mm. The tubes were insonated at an angle of 45 , with two-channel TCD instrumentation, 2-MHz insonation frequency, and a peak repetition frequency of 8 kHz (DWL Compumedics, Singen, Germany). The tubes were insonated through a 0.5-cm Plexiglas wall to mimic the effects of the human skull acoustic impedance Plexiglas 5 3.2 kg/m2 s; cortical bone 5 3.38 kg/m2 s (Bloomfield et al. 2000; Smitmans 2002). The transducer was secured with a specially designed Plexiglas holder. Each of the four tubes was
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insonated within a water bath with constant power and gain settings. To maximize the received Doppler power signals, for all recordings, the axial length of the sample volume was initially set to 4 mm when each of the respective tubes was placed under the transducer. It was then positioned until the maximum Doppler power signal was obtained using range gating. For Doppler power measurements, the axial length of the sample volume was extended to 10 mm for the 2-, 3- and 4-mm tubes and to 8 mm for the 1.5-mm tube. Optimizing the position of the sample volume enabled us to assume that the maximum beam intensity lay within the central region of the parabolic flow in the tube being studied, that is, the area of highest BFVs. Maximization of signal power was also necessary to ensure that the insonating beam intensity distribution was approximately equal for all tubes studied (Deverson and Evans 2000a). The high-pass frequency filter was set to a standard setting of 100 Hz. The measurements were recorded and averaged over a period of 10 s. Frequency-weighted firstmoment calculations of Doppler power were made using specially designed software (spectral power estimation within a spectrogram based on a 256-point fast Fourier transform with Blackman windowing and 50% spectral overlap). Velocity was measured and FI values were calculated automatically. Any offset in the FI/Vmax correlation slope was corrected by a calibration that vertically adjusted the line so that the slope passed through the zero intercept for velocity and FI (off-set calibration). Although both Vmax and Vmean provide information on blood flow values, when cross-sectional area is constant, Vmax is less sensitive to high-intensity artifacts in the spectrogram. Vmax values were therefore used to calculate flow and cross-sectional indexes. Relative measurements of change To enable the calculation of relative changes (percentage) in flow and area indexes, the FI value in the largest tube (4-mm diameter) was designated as 100% for each flow rate and Hct. Similarly, the AI values for the 4-mm-diameter tube, at the three flow rates and at each Hct, were designated as 100%. The FIs and AIs calculated for the other tubes were compared with these to determine the relative percentage changes as flow volume increased. Hematocrit values Heparinized whole blood with an initial Hct of approximately 60% from the same batch of AB Rhpositive blood was used for all recordings. The closedloop system was initially filled with 0.9% saline, and all gas bubbles were removed. Heparinized whole blood was added gradually to the system, and an equivalent volume of the blood-saline mixture was removed to
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obtain blood with different Hct values. Extreme care was taken not to introduce gas bubbles as blood was injected. Blood was allowed to flow through the system for at least 3 min before the recordings. Increasing Hct values were measured directly using a centrifuge (Hemokrit 4, Lic Instruments, Stockholm, Sweden) and Hct graph (Heræus Sepatech, Osterode/Harz, Germany). Doppler measurements were then carried out at the three different flow rates (150, 240 and 320 mL/min) and four different hematocrits (10, 20, 29 and 42%). Hematocrit was re-measured at the end of each set of recordings to ensure that it had not changed. RESULTS A strong linear correlation between calculated FI values and actual flow was found for each of the four insonated tube sizes at flow values of 150, 240 and 320 mL/ min (Fig. 1a–d). Each of the four graphs represents one of the defined Hct values (10%, 20%, 29% and 42%). Linear dependence was strong for all recordings, with a Pearson correlation coefficient greater than 0.95 for each tube (Table 1). The FI values obtained from the recordings were arbitrary, relative values and, as such, are not units are not given. The percentage change in FI values also correlated strongly and linearly with the actual flow measurements in all four tubes, at all flow rates and Hct values (all Pearson correlation coefficients .0.99). The correlation lines plotted for FI values and actual flow did not maintain a consistent position relevant to each other in the four graphs in Figure 1. For each new set of measurements, the relevant tube had to be placed below the fixed transducer. Despite the efforts described above, it was impossible to ensure that each of the tubes was in exactly the same position. Some small variation in tube position was inevitable, and this may have affected the power of the reflected Doppler signal. The speckling effect of RBCs on the backscattered Doppler echoes may also influence the Doppler power levels reflected at each Hct value, which may explain the random ordering of the plots of correlation between flow index and flow (Fig. 1). The calculated AI values varied by up to 8% as flow volume increased from 150 to 320 mL/min, even though both Hct and tube CSA remained constant. The calculated percentage changes in AI, normalized to the 4-mm tube values, exhibited a much smaller degree of deviation from actual CSA values (range: 0–2%, mean level of variation: 0.4%) (Table 2) when Hct was constant. A strong linear correlation between these relative changes in AI and the corresponding CSA values for all tubes was also observed (all Pearson correlation coefficients .0.99, all associated significance measures ,0.01). Figure 2(e–h) illustrates this linear dependence.
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Fig. 1. Correlation between flow index and flow (mL/min). The graphs indicate a strong correlation between calculated flow index (FI) values and actual flow (150, 240 and 320 mL/min) in the four tubes of different size. Each graph represents one of the defined hematocrit values: (a) 10%, (b) 20%, (c) 29%, (d) 42%. Hematocrits and tube diameters were constant for each set of recordings. Pearson correlation values are .0.99 for all plots. C 5 1.5-mm tube, : 5 2-mm tube, - 5 3-mm tube, A 5 4-mm tube.
The variation in FI values when Hct was increased from 10% to 42% was substantial; ranging from 25% in the 3- and 4-mm tubes to 76% in the 1.5-mm tube, even though both flow and tube CSA remained constant (Fig. 3i–l). Plots of either FI or AI versus Hct revealed an initial increase in the respective indices as Hct increased from 10% to 20%. A rise in Hct from 20% to 29% was associated with a reversal of this trend, and all FI values calculated at a Hct of 29% were lower than those calculated at a 20% Hct. A further increase in Hct, from 29% to 42%, was associated, in most of the studies, with a greater decrease in FI values. As Hct rose from 20% to 29%, the average decreases in FI values in the 4-, 3-, 2- and 1.5-mm tubes were 20%,
30%, 26% and 18%, respectively. With a further increase in Hct from 29% to 42%, the FI decreased by an average of 7%, 7.5% and 12% in the 4-, 3- and 2-mm tubes, respectively. For the 1.5-mm tube, there was a comparatively larger decrease in the FI of 28% as Hct rose from 29% to 42%. DISCUSSION This is the first in vitro study to find that calibrated, frequency-weighted TCD signal power measurements may be used to assess relative blood flow and crosssectional area changes. The FI/velocity off-set calibration described in this study minimized the influence of factors that negatively affect how uniformly the vessel is
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Table 1. Pearson linear correlation values (and significance measurements) for FI values versus actual flow for each of the four tube diameters at the four different hematocrit values* Pearson correlation for FI versus flow Diameter (mm) Hematocrit 10 Hematocrit 20 Hematocrit 29 Hematocrit 42 1.5 2 3 4
0.99y 0.98y 1 0.99y
1z 0.99y 1y 1y
1y 1y 0.99 0.99
1z 0.99y 1z 0.99y
* See Figure 1 and main text. y Significant, p $ 0.05. z Significant, p # 0.01.
insonated by the ultrasound beam. We also confirmed that both flow and area indexes are dependent on constant Hct values. The flow index used in this study was derived from an effective average Doppler power at each hematocrit level. Because of the large number of RBCs in the sampling volume there is an average distance between RBCs, and this average distance, varying with hematocrit level, effectively determines Doppler power and the effect of speckle on Doppler power. Plots of flow index versus flow (Fig. 1) revealed a random order of results associated with hematocrit value, which is consistent with the effects of speckle. These results support our definition of a flow index at a constant hematocrit, but also indicate the random results caused by speckle. A number of in vivo studies have used information from the full Doppler power spectrum in an effort to measure flow variation (Aaslid 1987; Aaslid et al. 1989; Poulin and Robbins 1996; Poulin et al. 1996). These studies did not, however, correct for the effects of inhomogeneous vessel insonation on the reflected Doppler power signal and the FI/velocity relationship. The theoretical relationship between Doppler signal power and vessel CSA is, among other things, Table 2. Percentage change in area index versus tube diameter as flow volume increases* Maximal change in area index (%) Diameter (mm) Hematocrit 10 Hematocrit 20 Hematocrit 29 Hematocrit 42 1.5 2 3 4
0 0 0 0
0 1 2 1
0 1 1 1
0 1 1 0
* Each of the 16 values in the table is the maximal percentage change in area index as flow rate increased from 150 to 320 mL/min. For each value, the hematocrit and tube diameter were constant. A relative change in the area index was calculated on the basis of flow index values. The area index values calculated for the 4-mm-diameter tube were designated as the 100% values. The area index values calculated for the other three tubes were normalized to these values.
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dependent on uniform insonation of the vessel. This is necessary to ensure correct weighting of the power signal reflected from RBCs moving at different velocities (Arts and Roevros 1972; Deverson and Evans 2000a; Hatab et al. 1997). In calculation of the FI, the power of the Doppler signals reflected from the various points within the vessel being insonated is weighted according to the Doppler frequency of the beam at each corresponding position. Variations in beam intensity will therefore lead to a variation in the weighting and a distortion of the received Doppler signal. Factors that lead to distortion of the ultrasound beam and, therefore, nonuniform vessel insonation include inhomogeneous tissue layering between the transducer and the vessel and, in particular, the temporal bone, which causes attenuation and refraction of the ultrasound beam and non-uniform insonation of the vessel (Deverson and Evans 2000a; Deverson et al. 2000; Fry and Barger 1978; Hatab et al. 1997). It has been observed that the extent of spectral power distortion is related to the shape of the ultrasound beam across the vessel (Deverson and Evans 2000a, 2000b). A correction factor for non-uniform insonation can be calculated for in vitro measurements when the vessel size is known (Deverson and Evans 2000a, 2000b). This is, however, not possible for in vivo recordings, where the diameter of the vessel is normally not known. We have therefore carried out a calibration of the off-set of the slope describing the correlation between the calculated FI and velocity values. The slope of the curve describing the relationship between these two parameters did not pass through zero with absent flow because of signal damping and the Plexiglas wall, which mimics the effects of the temporal bone on the ultrasound beam. The intercept of the correlation line between FI and maximum velocity V was therefore corrected to zero, with the gradient of the slope remaining unchanged. This is especially important for future clinical studies, as it has been shown that the degree of ultrasound beam distortion varies between patients (Deverson and Evans 2000a, 2000b). An automatic zero-intercept calibration of this correlation is therefore mandatory for each new set of measurements. Flow index and maximum velocity values were used to determine relative changes in cross-sectional area, as F 5 CSA 3 Vmax. We found a strong correlation between relative changes in AI values and corresponding CSAs. This contrasts with the findings of Giller et al. (1998), who found that Doppler spectral power measurements in arbitrary units gave varying AI values. Clinical measurements Potential weaknesses of this method, when applied in the clinical setting, include the effects of high-pass
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Fig. 2. Correlation between percentage change in area index and cross-sectional area (mm2). The graphs reveal that there was a strong correlation between percentage change in area index (AI) and change in cross-sectional area (CSA). Area indexes were calculated for each of the four tubes of different sized. Volume flow and hematocrit remained constant. Percentage changes in area indexes, relative to measurements for the largest (4-mm) tube, were calculated. Pearson linear correlation values are .0.99, with significance at p , 0.01 for all plots. Hematocrit: (e) 10%, (f) 20%, (g) 29%, (h) 42%. , 5 150 mL/min, > 5 240 mL/min, O 5 340 mL/min.
filtering and the need for both a constant Hct value and absolute stability of the transducer position to allow continuous measurement of the maximal Doppler power from the vessel. Movement of the TCD probe will lead to a loss of or decrease in the reflected Doppler power signal. Previous studies have reported that there is one optimal transducer position for the measurement of maximum power values and that the received power falls by more than 25% within 1 mm of this position (Deverson and Evans 2000a). Minimal movements of the transducer during clinical recordings can lead to an incorrect assessment of relative
blood flow changes. It is therefore essential, in the clinical setting, that the probe maintains a position where it measures the maximum reflected Doppler power signal from the vessel. It is hoped that the ongoing development of transducer devices that automatically maintain an optimal Doppler signal will help to resolve this very important problem (von Kruger and Evans 2002), allowing measurements with minimum contributions from voluntary or involuntary patient motion. High-pass filtering is used to attenuate lowfrequency components within the signal, such as those caused by slow vessel wall movement. Filtering will
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Fig. 3. Flow index versus hematocrit. The graphs illustrate the changes in flow indexes with rising hematocrit values, despite constant flow volume and tube diameter. Flow index initially increased and then decreased at hematocrit increased. Tube diameter: (i) 4 mm, (j) 3 mm, (k) 2 mm, (l) 1.5 mm. — 5 320 mL/min, ∙∙∙∙∙ 5 240 mL/min, - - 5 150 mL/min.
therefore have an effect only on the small number of RBCs close to the vessel wall with the lowest velocities. Frequency-weighted Doppler power measurements are focused on the higher velocities in the central part of the vessel lumen, further ensuring that any effect of filtering will be minimal. Indexes of relative blood flow changes based on variations in the ultrasound power reflected from RBCs are also affected by changes in Hct values. The relationship
between Hct and Doppler signal power is complex. At low Hct values, much lower than physiologic values, there is a linear relationship between increasing Hct values and increasing Doppler signal power, as the RBCs individually contribute to the reflected signal power. At higher Hct values, the RBCs begin to aggregate, and the assumption that each RBC is contributing to the reflected ultrasound power is no longer true (Oates 2001). An increase in Hct above 28% leads to a decrease in the received
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Doppler power signal because of a change in the scattering coefficient of the blood. Despite this, it has been postulated that even at higher, physiologic Hct values, the power of the received Doppler power signal can still be used to measure relative changes in blood flow and CSA, provided the Hct remains constant (Deverson and Evans 2000a, 2000b). This hypothesis has, however, not been previously confirmed. Our results clearly indicate that Doppler power is affected by changing Hct values. FI values increased as Hct values rose from 10% to higher values and decreased when Hct increased above 29%. We did, however, find that the calculated FI values were strongly correlated with actual flow within a wide range of constant Hct values, including those in the normal, physiologic range. In most clinical situations, Hct will not change. This may not be the case when TCD is used to monitor intracranial hemodynamics during surgery, where both blood loss and intravenous fluid therapy are common. We have assumed that change in flow values or acceleration of RBCs does not have a significant effect on the reflected Doppler power and its instantaneous spectral distribution. These instantaneous index calculations are based on frequency-weighted power measurements using one fast Fourier transform process within 20 ms. The red blood cell velocities can be assumed to be constant with no significant changes in Doppler frequency. Furthermore, although the echogenicity of blood may vary during pulsatile flow, Doppler power does not vary significantly during pulsatile cycles or changes in flow rates (Paeng et al. 2001). The indexes calculated in this study exhibited a good correlation in a range of different actual flow rates and cross-sectional areas when hematocrit values were constant. Finally, we used the TCD instrumentation to calculate the indexes described because of the specific difficulties involved in measuring changes in blood flow in the relatively small vessels throughout the skull. In this situation the ultrasound transducer can be maintained in an almost constant position at the temporal bone acoustic window. The methods and conclusions can, however, be applied to vascular ultrasound in general, provided the transducer position and, therefore, damping of the ultrasound in the tissue remains constant with respect to the insonated vessel. CONCLUSIONS This is the first in vitro study to find that calibrated, frequency-weighted trans-cranial Doppler signal power measurements may be used to assess relative blood flow and cross-sectional area changes; however, these measurements are dependent on constant hematocrit values.
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Acknowledgments—S. Wallace and N. Logallo each received research grants from the Norwegian Foundation for Health and Rehabilitation.
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